Answer:
Step-by-step explanation:
a₁₂ = a₁r¹²⁻¹ = -15×6¹¹
Find the length of ST
Answer:
ST = 10
Step-by-step explanation:
Δ RSQ and Δ RTP are similar by the AA postulate , then
the ratios of corresponding sides are in proportion , that is
[tex]\frac{RS}{RT}[/tex] = [tex]\frac{RQ}{RP}[/tex] ( substitute values )
[tex]\frac{5}{RT}[/tex] = [tex]\frac{9}{9+18}[/tex] = [tex]\frac{9}{27}[/tex] = [tex]\frac{1}{3}[/tex] ( multiply both sides by 3 to clear the fraction )
RT = 3 × 5 = 15
Then
ST = RT - RS = 15 - 5 = 10
Anyone know part B to this?? (Will give all stars!) please help
Answer: c -2
Step-by-step explanation:
y=-2x+3
-2 is the slope because y= mx+b and m is the slope
Answer:
a) D [-2x +3] | b) D [-2]
Step-by-step explanation:
Get it into the form y=mx+b
To do this subtract 2x from 2x+y=3 to get y= -2x+3
-------------------------------------------------------------------------------------------------------------
Part B: Find the slope
The slope is the coefficient in front of the x in the slope-intercept form.
In this case, it is -2.
Therefore, -2 is the slope of the line.
Answers: [-2x + 3] and [-2]
Which is the mode for the data set? -1,0,3,4,-3,-1
Mode of data set -1, 0, 3 ,4, -3, -1 is - 1 with most often in data set.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The data set is,
⇒ -1, 0, 3 ,4, -3, -1
Now, We know that;
The mode is the value that appears the most often in the data set.
Here, In the data set - 1 is most often number.
So, The mode of data set = - 1
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21⁄2
yards of thread to make 4⁄6
of a sock. How many yards of thread will it take to
make an entire sock?
The yards of thread that will take to make an entire sock will be 3 3/4 yards.
How to calculate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
In this case, 2 1/2 yards of thread to make 4 /6
of a sock.
The yards of thread that will take to make an entire sock will be:
= 2 1/2 ÷ 4 / 6
= 5 / 2 × 6/4
= 30 / 8
= 15 / 4
= 3 3/4 yards.
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the peak shopping time at a pet store is between 8-11:00 am on saturday mornings. management at the pet store randomly selected 95 customers last saturday morning and decided to observe their shopping habits. they recorded the number of items that a sample of the customers purchased as well as the total time the customers spent in the store. identify the types of variables recorded by the pet store.
The number of items is discrete and the total time is a continuous variable recorded by the pet store.
The two things recorded by the pet store;
first is the number of items purchased and another is the time between the given interval of 8 am to 11 am.
we know that
the number of items was counted so it will be discrete and the total time was measured so it will be a continuous variable.
Therefore, the types of variables recorded by the pet store are the number of items as a discrete variable and the total time as a continuous variable.
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3(4x-10)= 2(3x-30) help
The solution to the equation 3(4x-10) = 2(3x-30) is x = -5.
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.
Let's solve for x:
3(4x - 10) = 2(3x - 30)
First, we can simplify both sides by distributing the coefficients:
12x - 30 = 6x - 60
Next, we'll move all the x terms to one side of the equation and the constants to the other side:
12x - 6x = -60 + 30
Simplifying further:
6x = -30
Finally, we can solve for x by dividing both sides by 6:
x = -5
Therefore, the solution to the equation 3(4x-10) = 2(3x-30) is x = -5.
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Angles 3 and 4 are supplementary. The measure of angle 3 is
thirty-five more than one-fourth the measure of angle 4.
1. What is the measure of Angle 3?
2. What is the measure of Angle 4?
The values of ∠4 and ∠3 are 116 degrees and 64 degrees respectively.
Given ,
What are supplementary angles ?
The angles are said to be in supplementary if and only if the sum of two angles is 180 degrees .
Angles 3 and 4 are supplementary.
The measure of angle 3 is
thirty-five more than one-fourth the measure of angle 4.
So,
∠3 + ∠4 = 180 degrees.
∠3 = 180-∠4 - equation 1
∠3 = 35 + (1/4 ) ∠4 - equation2
As equation 1 and 2 are equal
hence,
180-∠4 = 35 + (1/4) ∠4
180-35 = ∠4 + (1/4) ∠4
145 = ((1/4)+1) ∠4
145 = (5/4) ∠4
∠4 = 145 * 4 / 5
∠4 = 29*4
∠4 = 116
∠3 = 180-116
∠3 = 64
Hence the values of ∠4 and ∠3 are 116 degrees and 64 degrees respectively.
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Find the value of x in the
following parallelogram:
2x - 5
X + 10
x=[?]
The value of x in the following parallelogram is 15
What is a parallelogram?You should recall that a parallelogram is a quadrilateral whose opposite sides are equal and parallel
The given sides are
2x - 5 and X + 10This means that
X + 10 = 2x -5
Collecting like terms we have
x-2x = -5-10
-x = -15
Dividing by -
We have x= 15
Therefore x is 15 in the parallelogram.
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solve the inequality 27>b+57
Answer:
b < -30
Step-by-step explanation:
27 > B + 57 Subtract 57 from both sides
27 - 57 > b +57 - 57
-30 > b
or
b < -30
the volum of the wood in a tree varries directly as height and the square of length
Answer:
The volume of wood in a tree varies directly with the height and the square of the length of the tree. This means that if we increase the height of the tree, the volume of wood in the tree will also increase, and if we increase the length of the tree, the volume of wood will increase by the square of that increase.
This relationship can be expressed mathematically as:
V = khl^2
Where V is the volume of wood in the tree, h is the height of the tree, l is the length of the tree, and k is a constant of proportionality.
This relationship is based on the assumption that the cross-sectional area of the tree remains constant, and that the volume of wood in the tree is directly proportional to the height and the square of the length of the tree.
measurements of angles
Step-by-step explanation:
10x + 17 + 8X - 31 + 6x - 8 = 180
Use this equation and solve this equation and you will find the answer
57. In the standard (x,y) coordinate plane, define the
h-v distance between. 2 points to be the length, in
coordinate units, of the shortest path between the
2 points using only horizontal and vertical segments.
The expression (5-2) +13-(-4) gives the
h-v distance between which of the following pairs of
points?
A.(3, 5) and (-4, 2)
B.(3, 5) and (-2,-4)
C. (5.-4) and (-2, 3)
D. (5,-2) and (3, 4)
E. (5, 2) and ( 3,-4)
A vertical line in geometry is one that crosses the page from top to bottom.
What is meant by horizontal and vertical segments?A vertical line in geometry is one that crosses the page from top to bottom. Its cousin is the horizontal line that spans the page from left to right. A horizontal line and a vertical line are perpendicular.
Businesses utilize segmentation as a marketing strategy to focus on a certain market segment or type of customer. While vertical segmentation sharpens your marketing emphasis to target customers in a smaller demographic, horizontal segmentation entails offering a product to a broad range of consumers.
A horizontal object is one that is perpendicular to the horizon. Due to the fact that vertical is the polar opposite of horizontal, anything that forms a 90° (right angle) with either the horizontal or the horizon is referred to as vertical. This means that the horizontal line is one that crosses from left to right. Mathematical applications of the horizontal and vertical.
Therefore, the correct answer is option C. (5.-4) and (-2, 3).
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The figure below is composed of square ABCD and equilateral triangle
Answer: 225°
Step-by-step explanation:
The correct option is D)
Refer Figure
Given:
ABCD is a square
ABP is an equilateral triangle
AB=BP=BC (△ABP is equilateral and AB and BC belong to a square, hence all are equal)
∠ABC=∠ABP+∠PBC=60°+∠PBC
90°−60°=∠PBC
∠PBC=30°
In △BPC
BP=BC
∠BPC=∠BCP= 2
180−∠PBC
( angles opposite to equal sides of a triangle are equal)
∠APC=∠APB+∠BPC=(60+75)°=135°
Hence, Reflex ∠APC=(360−135)°=225°
The sum of the two digits number is nine
If the sum of two digits t and u is t + u = 9, then the second equation is option 2: t = 1/2 u.
What is a digit?
In math, single integers called digits are used to represent values. To represent all mathematical values, the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are employed in various combinations and repetitions.
The first equation is as given t + u = 9
Second equation t = u/2 since the number in the tens position is one half of the one in the units. So if you divide u by two, you should have one t, as the equation states.
The second equation is t = (1/2)u => u = 2t
When we replace this in first equation we get -
t + 2t = 9
3t = 9
t = 9/3
t = 3
When we replace it again in the equation -
u = 2 t
= 2 · 3
= 6
The requested number is 36.
Therefore, the number is 36 and the second equation is t=u/2.
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Let f(x) 1 -x^2/3. Show that f(- 1) = f(1) but there is no number c in ( -1, 1) such that f'(c )= 0. Why does this not contradict Rolle's Theorem?
Therefore , the solution to the given problem of function comes out to be ss a result, Rolle's Theorem remains true.
What does the word function mean?Mathematics deals with numbers and their variants, formulae and associated structures, geometries and their areas, and locations where they might be found. The term "function" describes the connection between a group of input, of which each has a corresponding output. A function is an association among inputs and outputs where each input results in a single, unique output. A realm as well as a codomain, or scope, are assigned to each function. Functions are typically denoted by the letter f. (x). The input is an x. On activities, one-to-one activities, many-to-one functions, within operations, and on functions are the four main categories of functions that are available.
Here,
Consider
f(-1)=1-[tex](-1 )^{\frac {2}{3}}[/tex]=0
and f(1)=1-[tex](-1 )^{\frac {2}{3}}[/tex]=0
So, f(-1)= f(1) (1)
As a result of differentiating f(x) with regard to x, we now have
f'(x)= -2 / 3
Consequently, f'(0) is false.
So, at 0inleft (-1,1 ), f cannot be deduced.
Therefore, the given function in the range (-1,1) does not satisfy Rolle's theorem.
As a result, no c exists in (-1,1) for which f'(c )=0 even though f(-1)=f(1 ).
As a result, Rolle's Theorem remains true.
Therefore , the solution to the given problem of function comes out to be ss a result, Rolle's Theorem remains true.
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Please hep pls easy easy proportional relationship
Answer:
Below
Step-by-step explanation:
A) Juan reads at 57 pages /hr
B) Juan reads 9 pages more per hour (57-48) than Lexi
in 7 hours this will be 7 hr * 9 p/hr = 63 pages
Solve the formula A=1/2(a+b) for a
The equation for a is a=2A-b
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here: A=1/2(a+b)
a=2A-b
Hence, the equation for a is a=2A-b
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What’s the tangents ratio for F?
5/4
5/3
4/3
3/4
The tangent ratio of F by using the rule from trigonometry is 4/3
What is the trigonometry ratio?Trigonometric ratios are ratios that represent the length of a triangle's sides. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the fundamental trigonometric ratios.
The sine of the trigonometry ratio is sin θ = opposite/hypotenuse. The cosine of the trigonometry ratio is cos θ = adjacent/hypotenuse. The tangent of the trigonometry ratio is tan θ = opposite/adjacent. From the image given. The opposite side is the line facing the angle F;
Thus, the opposite side = 8, and the adjacent is the smallest side, which is 6.
Therefore, the tangent ratio for F is:
tan θ = 8/6
This can be reduced to 4/3
Therefore, we can conclude that the tangent ratio of F is 4/3.
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Calculate the given angle, to the nearest degree,
55
33
44
Answer:
Step-by-step explanation:
1 radian is equal to 180^0/Pi
[tex]55=55*\frac{180}{\pi y} \\=54.97787[/tex]
Equivalent fractions to 30/10
Answer: 3/1. 6/2. 9/3. 12/4. 15/5. 18/6. 21/7. 24/8. 27/9 and many more
Step-by-step explanation:
Heyo, looking for some help please :)
The midpoint of AB = ([?], [])
When A point is (3, 1) and B point is (-1 , -1), the midpoint of AB is ( 2, 1) . The line segment's exact midway is where the midpoint is located.
what is mid point ?The term "midpoint" describes a point along a line that connects two points. The midway is situated between the two reference locations, which are the line's ends. The line connecting these two places is split into two equally sized sections by the middle. A point that splits a line segment into two equal halves is known as the midway. In other words, the line segment's exact midway is where the midpoint is located. It is demonstrably true that the middle of a number line has the same value as the average of any two matching places on the line.
given
midpoint of AB is equal to (x2 - x1) / 2 (3 + 1) / 2 = 2.
the midpoint of AB is 1
the midpoint of AB is (y2 - y1)/2
= (1+1)/2.
= ( 2 ,1 )
When A point is (3, 1) and B point is (-1 , -1), the midpoint of AB is ( 2, 1) .
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Find the solution of the given initial value problem. y'-y=3te^2t , y(0) = 1
y(t)=?
Determine the value of x
The value of the x is 11.
What are vertically opposite angles?
Opposite angles are the angles directly opposite each other where two lines cross. The intersection point is called the vertex, which is where the lines connect to form the angle. Opposite angles are also called vertical angles. In this instance, the word vertical refers to the vertex as opposed to direction.
We have given,
Two opposite angles:
(6x + 1)°, and 67°
So, We need to determine the value of x.
We know that the property of opposites angles, which the opposite angles are equal to each other.
So, (6x + 1)° = 67°
By calculating further:
6x + 1 = 67
6x = 67 - 1
6x = 66
x = 66/6
x = 11
Hence, the value of the x is 11.
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Help Its geometry, I'm struggling
Answer:
[tex]y=\frac{3}{4}x-\frac{7}{2}[/tex]
Step-by-step explanation:
[tex]m_{\parallel}=\frac{3}{4} \\ \\ y-1=\frac{3}{4}(x+6) \\ \\ y-1=\frac{3}{4}x-\frac{9}{2} \\ \\ y=\frac{3}{4}x-\frac{7}{2}[/tex]
can someone help me with this please?
could the answer be;
a.) px=-3x^3-2x²-6x-16,r(x)=-45, and q(x)=x-3
b.) px=-3x^3-2x²-6x-16,r(x)=-117, and q(x)=x-3
c.) px=-x^3+4x²+12x+16,r(x)=-117, and q(x)=x-3
d.) px=-x^3+4x²+14x+45,r(x)=-0, and q(x)=x-3
The simplest form of the given expression is px=-3x^3-2x²-6x-16,r(x)=-45, and q(x)=x-3.
What is polynomials?
Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.
(-x^4+7x^3+2x+3)/ (x-3)
=-x² + 4x² + 12x + 38 + 117/(x - 3)
Hence the simplest form of the given expression is px=-3x^3-2x²-6x-16,r(x)=-45, and q(x)=x-3.
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Write f(x) = |x + 3| as a piecewise function.
Answer:fx
Step-by-step explanation:
suppose we want to choose 7 objects without replacement from 11 distinct objects  how many ways can this be done if the order of the choices is relevant
In 1663200 ways objects can be chosen if the order of the choices is relevant. The solution has been obtained using permutation.
What is permutation?
An arrangement of items in a specific manner or sequence is referred to as a permutation. It is important to think about both the selection and the arrangement when dealing with permutation. Briefly put, permutations depend much on ordering. In other words, a permutation is a combination that is ordered.
We want to choose 7 objects without replacement from 11 distinct objects
So, since the order of the choices is relevant, we will use permutation.
Therefore,
⇒nPr = n! ÷ (n - r)!
⇒11P7 = 11! ÷ (11 - 7)!
⇒11P7 = 11! / 4!
⇒11P7 = (11 * 10* 9 * 8 * 7* 6 * 5)
⇒11P7 = 1663200 ways
Hence, in 1663200 ways objects can be chosen if the order of the choices is relevant.
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Which expression is the least absolute value |-28| |-1| |6| |15|
Answer: |-1|
Step-by-step explanation:
So lets just solve all of this stuff so you can just look at it and get the answer. | - 28 | = 28, |-1| = 1, |6| = 6, |15| = 15. So we have 28, 1, 6, and 15. Put this in order we have: 28, 15, 6, 1 which means 1 is the least or your could say |-1| is the least. Have a good day ;)
Can somebody please tell me how to Solve Systems by Elimination? I don't understand it at all and I'm staying up all night trying to figure it out. I especially don't understand the co-efficient part.
An example is:
2c+3d=12
5c-d=13
What would the answer be to that? Please provide an explanation!
Solving the example, hope it will help you with better understanding.
Given system:
2c + 3d = 125c - d = 13We need to eliminate one of the variables c or d. Let us eliminate d.
We see the first equation has 3d and the second equation has - d. The coefficients of d are 3 and - 1. If we multiply the second one by 3 it will become - 3, then if we add them up they will cancel, 3d - 3d = 0. By doing this we'll eliminate the variable d and left with variable c in the resulting equation.
Demonstrating how it works:
2c + 3d = 12, we leave it as is
5c - d = 13, we multiply all terms of this by 3, it becomes, 15c - 3d = 39
Now add up the two equations:
2c + 15c + 3d - 3d = 12 + 39, eliminated d17c = 51 solving for cc = 51/17c = 3Now we can find the value of d:
2c + 3d = 122*3 + 3d = 126 + 3d = 123d = 6d = 2Our solution is:
c = 3, d = 2The answers please I need the answers I’ll give points
Answer:
Step-by-step explanation:
1) m∠1 = m∠2
4x - 1 = 2x + 7
2x = 8
x = 8/2 = 4
2) m∠1 = (m∠YWX) / 2 = 62/2 = 31
3) AB is 4 squares long. Start at A, go over 2 squares, then draw a line straight up to point C.
4) Altitude is the height of a triangle. Find the midpoint of the bottom line, then draw a line straight up to the vertex (top of the triangle). Your drawn line should form a right angle with the bottom line.